Utilisation and conservation of farm animal genetic resources 149
Chapter 7. Genetic contributions and inbreeding
to non-additive gene actions, hence their association with inbreeding depression. Expression of inbreeding depression is oten through deleterious recessive alleles, where
inheriting two copies of an allele results in a lack of function, whilst inheriting 1 or 2 copies of the alternative allele results in near normal function. Depression is not the
only consequence of inbreeding, and in breeding schemes it is oten the large changes in allele frequency that result from a high ΔF that are important to manage. ΔF may be
regarded as a measure of risk in a breeding scheme and Woolliams
et al. 2002 develops this idea further.
It is valuable to consider how a layman may empirically recognise a potential inbreeding problem, or examine whether inbreeding may be a likely explanation for an observed
problem in itness. A irst step may be to obtain several pedigrees back to the 8 great- grandparents and see how many and how oten ancestors are common to both the
maternal and paternal side for each individual. his will indicate a non-zero probability of identity by descent F 0 for any locus in the individual. Examination of the whole
group of individuals may show the same great-grandparents recurring repeatedly in the pedigree. What is being noted is that a large proportion of the pathways in the genealogical
tree of the population trace back to the same small handful of contemporary ancestors. here may be two reasons for this: there are only very few ancestors in this ancestral
generation or there are many other ancestors but each of these others has relatively very few pathways leading down to the current population. In a heuristic way, deine r
i
, as the proportion of genes tracing back to each of the ancestors in the generation, and
note that the sum of these proportions must be 1 because we are dividing the total gene low between the ancestors. From the above arguments, we might be concerned if the
average ‘r
i
’ is large, or if the r
i
are highly variable, or both. Consequently an empirical measure of risk would increase as the average and the variance of the r
i
increase, and one function which increases in this way is the sum of squares of the r
i
, denoted Σ r
i 2
. his empirical examination is looking at the impact of just one generation, and so it is
a measure of a rate of increase per generation, since the total inbreeding will depend on the accumulation of such efects over multiple generations. herefore, a highly intuitive
measure of a rate of inbreeding, ΔF, is related to the sum of squared proportions, or contributions, by a generation of ancestors to their living descendants.
2. Genetic contributions
he long-term contribution, r
i
, for an ancestor i is the proportion of genes in population derived from i by descent many generations later. Note it deals only with relationship
derived by descent, so for example one full-sib makes no genetic contribution to another even though they have a relationship coeicient 0. A conceptual way of thinking
about the long-term genetic contribution is that it represents the contribution of an
150 Utilisation and conservation of farm animal genetic resources
John Woolliams
individual’s Mendelian sampling term to the long-term gene pool. his is useful because the Mendelian sampling is the unique bit of genetic variation that the individual brings
to the population. he idea of the contribution of the Mendelian sampling term helps towards recognising that the gene pool of the future has contributions from all ancestors
and not just the founders.
Figure 7.1 shows a small pedigree. In each generation of descendants the contributions of the ancestors to the group can be calculated. Over time, say 5 to 10 generations,
these contributions converge and show no further change over time, and it is these converged contributions that are the long-term contributions. he contributions r
i
will difer between the ancestors, are all ≥ 0, and will sum to 1 since a single generation of
ancestors must explain the whole gene pool. he contributions of the ancestors A … D to the descendants M … P for the pedigree in Figure 7.1 are shown in Table 7.1: they
can be calculated by working down the pedigree following the rules a ancestors A to D contribute 1 to themselves, 0 to the other contemporary ancestors, b an ofspring
in any generation is the average of the contributions of A to D to its sire and dam.
A B
C D
E F
G H
I J
K L
M N
O P
Figure 7.1. An example pedigree: shaded and unshaded boxes represent the two sexes.
Table 7.1. Contributions from ancestors A, B, C, D to M, N, O, P.
A B
C D
M, N, O ⅜
⅛ ¼
¼ P
⅜ ⅛
⅜ ⅛